[EM] Is no Clones rule but EMers that it was used?
Markus Schulze
markus.schulze at alumni.tu-berlin.de
Tue Jan 14 12:25:01 PST 2003
Dear Craig,
you wrote (15 Jan 2003):
> So, that quoted text ("Statement 2 is only needed...") is around the
> topic of the second part.
>
> The third person grammatical category of pronouns and verbs is
> present in the text there. I enter that into the records. Given the
> wording, which of these is the case?:
> * "is only needed" refers to the designer's intent ?, or
> * it is implied by some detail proof that was missing.
That's a matter of taste. Those situations where all voters are indifferent
about all candidates can be excluded in the definition of "clones". If you
don't want to exclude these situations in the definition of "clones" you
can exclude these situations in the definition of "independence from clones".
If you want to exclude these situations neither in the definition of "clones"
nor in the definition of "independence from clones" then you can exclude
these situations in your general statements. For example: "Tideman's Ranked
Pairs method meets independence from clones except for those situations
where all voters are indifferent about all candidates."
You wrote (15 Jan 2003):
> "Only" means only (?).
"Only" means only. No other situations have to be excluded. This follows
from the fact that there are methods that meet independence from clones
as defined in my 13 Jan 2003 mail.
You wrote (15 Jan 2003):
> I never got information on what you meant by "decisive". Please e-mail
> in the perfectly exact algebraic/etc definition of "decisive [winner-set
> results].
In my 13 Jan 2003 definitions of "clones" and "independence from
clones" the term "decisive" doesn't occur.
You wrote (15 Jan 2003):
> Then that absolute majority method violates a right number of winners
> rule inside of this polytope:
>
> (([a+b+f]/2<a)([a+b+f]/2<b) or ([a+b+f]/2<a)([a+b+f]/2<b))
>
> I ask Mr Schulze to identify which of the 3 variables, is the "Voter".
>
> What suppose I wrote the rule like this (Mr Schulze) ?:
>
> (Method passes) = ((a+b+f<2a)(a+b+V<2b) or (a+b+f<2a)(a+b+V<2b))
>
> Now it has Schulze's V in it.
>
> I wonder if Mr Schulze would now tell the select audience of the
> Politicians and Polytopes mailing list, whether V can be a voter ?.
I have no idea what you are talking about.
Markus Schulze
******************************************************************
> From: Craig Carey <research at ijs.co.nz>
> Date: Wed, 15 Jan 2003 08:42:58 +1300
> Subject: Neo-Tideman-isms resurface to a final defence
>
> It seems that the thread will be split into 2 halves over 2 mailing
> lists. It is not as if the Election Methods List members are astute
> enough to remind that a person is not ballot paper or a vote.
>
> | From: Markus Schulze <markus.schulze at a...>
> | Date: Sun Jan 12, 2003 10:18 pm
> | Subject: Re: [EM] Is no Clones rule but EMers that it was used?
> ...
> | My definition of "clones" looks as follows:
> |
> | > Definition ("clones"):
> | >
> | > A[1],...,A[m] are a set of m clones if & only if the following
> | > two statements are valid:
> | >
> | > (1) For every pair (A[i],A[j]) of two candidates of this set,
> | >
> | > for every voter V, and
> | >
> | > for every candidate C outside this set
> | >
> | > the following two statements are valid:
> | >
> | > (a) V strictly prefers A[i] to C,
> | > if & only if V strictly prefers A[j] to C.
> | > (b) V strictly prefers C to A[i],
> | > if & only if V strictly prefers C to A[j].
> | >
> | > (2) For every candidate A[k] of this set and
> | > for every candidate D outside this set
> | > there is at least one voter W, who either
> | > strictly prefers A[k] to D or strictly prefers D to A[k].
> |
> | Statement 2 is only needed to exclude situations where all voters
> | are indifferent about all candidates. In this situation each neutral
>
> V is a list of symbols. It is inexplicable why there is no weights
> associated with the values named V.
>
> | election method is necessarily identical to "Random Candidate". And
> | obviously "Random Candidate" can be manipulated by running a large
> | number of identical candidates.
> |
> | "Independence from Clones" says that if a given set of clones
> | (A[1],...,A[m]) is substituted by a single macro-candidate A such that
> |
>
> There is even an attempt to clarifying the statement:
>
> "Statement 2 is only needed to exclude situations where all
> voters ...".
>
> So, that quoted text ("Statement 2 is only needed...") is around the
> topic of the second part.
>
> The third person grammatical category of pronouns and verbs is
> present in the text there. I enter that into the records. Given the
> wording, which of these is the case?:
> * "is only needed" refers to the designer's intent ?, or
> * it is implied by some detail proof that was missing.
>
> "Only" means only (?).
>
> --------------
>
> Winning with an absolute majority:
>
> A dictionary says (approximately):
>
> First Past the Post is where a candidate wins with a
> simple majority,
> instead of with an
> absolute majority.
>
> . A. a0
> . AB ab
> . B. b0
> . BA ba
> . {} f
>
> Also: a=a0+ab, b=b0+ba
>
> With an absolute majority:
>
> (A wins) <= ([a+b+f]/2<a)
> (B wins) <= ([a+b+f]/2<b)
>
> Change the "implied by" signs into "equals"
>
> Then that absolute majority method violates a right number of winners
> rule inside of this polytope:
>
> (([a+b+f]/2<a)([a+b+f]/2<b) or ([a+b+f]/2<a)([a+b+f]/2<b))
>
> I ask Mr Schulze to identify which of the 3 variables, is the "Voter".
>
> What suppose I wrote the rule like this (Mr Schulze) ?:
>
> (Method passes) = ((a+b+f<2a)(a+b+V<2b) or (a+b+f<2a)(a+b+V<2b))
>
> Now it has Schulze's V in it.
>
> I wonder if Mr Schulze would now tell the select audience of the
> Politicians and Polytopes mailing list, whether V can be a voter ?.
>
> The V in my equations was a real number (seemingly). The V of
> Schulze was a "Voter". My V can be converted from a real number
> to a paper, by uniting the value (='weight') with the empty
> preference list (V=f, and there were f spoiled ballot papers).
>
> To continue, where can the reality of the real word come from.
> Perhaps he voters. Indeed they have no names, but at least we
> have the letter V, the exploded rule of Mr Schulze (a thing that
> never checked for correctness), and it now Schulze may want to
> reassert that he overlooked the demise of the rule. The theorist
> before the rules: to lose the undefined rule before the theorist
> that advocated makes it a bit untruthful. I am sure Mr Schulze
> understands me. Mr Schulze was thinking wrong as early as 1998
> and if members know anything then they can post up the data.
>
> But to draw a correspondence with the V in my example, they
> would be people voting with spoiled ballot papers. Where is the
> principle that people that cast voters with integral discretized
> votes, can't be regarded mathematically as a continuously
> minutely adjustable quota that is real valued and of the
> axis or vertex indicated by its vote.
>
> Obviously with a paper being the empty ballot paper, is it
> disagreeable to plot every kind of method after using FPTP-izms
> or pairwise comparing -izms, to reduce the number of dimensions.
>
> I suppose Mr Schulze might be unconvinced that the word "Voter"
> implies discretizing. I never got information on what you meant
> by "decisive". To be guided by only the English meaning, it
> would seem that it might compete with my rule saying that "the
> number of winners shall be right" (i.e. what was required
> beforehand; with multivalued results being fully OK (while not
> actually occurring)).
>
> The premise was the Clones rule and there was a conclusion over
> "decisiveness". Please e-mail in the perfectly exact algebraic/etc
> definition of "decisive [winner-set results].
>
> I am sure that if Mr Schulze had of had a better rule he might
> have provided it. However seeing the lack of defence that the
> bad ones get as they get trampled under i(albeit under a fair
> treatment) is a little interesting.
>
> G. A. Craig Carey
----
For more information about this list (subscribe, unsubscribe, FAQ, etc),
please see http://www.eskimo.com/~robla/em
More information about the Election-Methods
mailing list